Related work: The Giry monad was introduced by Giry in [1]}. This monad and the finitely additive variation of it already have been constructed as codensity monads of inclusion functors of certain convex spaces in the category of measurable spaces by Avery in [2]}. The constructions we will present are different but related to Avery's constructions. The Radon monad originates from work by Semadeni [3]} and Swirszcz [4]} and is further discussed in [5]} and [6]}. The bounded Lipschitz monad is similar to the Kantorovich monad on the category of compact metric spaces, which was introduced by van Breugel in [7]}. This monad was extended to a monad on complete metric spaces by Perrone and Fritz [8]}, [9]}.
